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In mathematics, the Eisenstein ideal is an ideal in the endomorphism ring of the Jacobian variety of a modular curve, consisting roughly of elements of the Hecke algebra of Hecke operators that annihilate the Eisenstein series. It was introduced by Barry Mazur (1977), in studying the rational points of modular curves. An Eisenstein prime is a prime in the support of the Eisenstein ideal (this has nothing to do with primes in the Eisenstein integers).
In mathematics, the Eisensteinideal is an ideal in the endomorphism ring of the Jacobian variety of a modular curve, consisting roughly of elements of...
review Eisenstein's criterion EisensteinidealEisenstein integer Eisenstein prime Eisenstein reciprocity Eisenstein sum Eisenstein series Eisenstein's theorem...
In mathematics, the Eisenstein integers (named after Gotthold Eisenstein), occasionally also known as Eulerian integers (after Leonhard Euler), are the...
This proof was carried in his seminal paper "Modular curves and the Eisensteinideal". The ideas of this paper and Mazur's notion of Galois deformations...
number, together with the zero ideal. Primitive ideals are prime, and prime ideals are both primary and semiprime. An ideal P of a commutative ring R is...
Company. pp. 205–246. Mazur, Barry (1977). "Modular curves and the Eisensteinideal". Publications Mathématiques de l'IHÉS. 47 (1): 33–186. doi:10.1007/BF02684339...
a principal ideal domain, or PID, is an integral domain (that is, a commutative ring without nonzero zero divisors) in which every ideal is principal...
Granville: 81–100. MR 1330929. Mazur, Barry (1977). "Modular curves and the Eisensteinideal". Publications Mathématiques de l'IHÉS. 47 (1): 33–186. doi:10.1007/BF02684339...
In algebraic number theory Eisenstein's reciprocity law is a reciprocity law that extends the law of quadratic reciprocity and the cubic reciprocity law...
Amer. J. Math. 70 (1948), 31–74. B. Mazur. Modular curves and the Eisensteinideal, Inst. Hautes Études Sci. Publ. Math. 47:33–186, 1977. This formula...
Gordon and remains unsolved. Algebraic integer Cyclotomic field Eisenstein integer Eisenstein prime Hurwitz quaternion Proofs of Fermat's theorem on sums...
cube root of unity), the ring of Eisenstein integers. Define f (a + bω) = a2 − ab + b2, the norm of the Eisenstein integer a + bω. K[X], the ring of...
{p}}}} for any prime ideal p {\displaystyle {\mathfrak {p}}} of Z[ζ]. It is extended to other ideals by multiplicativity. The Eisenstein reciprocity law states...
see Fundamental theorem of arithmetic), the Gaussian integers and the Eisenstein integers are UFDs. If R is a UFD, then so is R[X], the ring of polynomials...
generalized, from the quadratic reciprocity law and the reciprocity laws of Eisenstein and Kummer to Hilbert's product formula for the norm symbol. Artin's result...
example is the non-real cubic root of unity −1 + √−3/2, which generates the Eisenstein integers. Quadratic integers occur in the solutions of many Diophantine...
In algebra, the congruence ideal of a surjective ring homomorphism f : B → C of commutative rings is the image under f of the annihilator of the kernel...
Some of these examples are listed in Artin, Algebra (2nd ed.), §13.8. Eisenstein–Kronecker number Genus character Heegner number Infrastructure (number...
described in a 1987 article by S. M. Eisenstein and C. R. Parry of Witwatersrand University. Computerized tomography is the ideal for typifying facet joint arthrosis;...
suppressed and believed destroyed before its completion. Directed by Sergei Eisenstein, it tells the story of a young farm boy whose father attempts to betray...
biquadratic reciprocity law. Jacobi and Eisenstein at around the same time proved a cubic reciprocity law for the Eisenstein integers. The study of Fermat's last...
multiplication by units). Similarly, in 1844 while working on cubic reciprocity, Eisenstein introduced the ring Z [ ω ] {\displaystyle \mathbb {Z} [\omega ]} , where...
ISSN 0303-1179, MR 1141458 Mazur, Barry (1977), "Modular curves and the Eisensteinideal", Publications Mathématiques de l'IHÉS (47): 33–186, ISSN 1618-1913...
{2\pi \imath }{3}}.} The ring of Eisenstein integers is Z [ ω ] . {\displaystyle \mathbb {Z} [\omega ].} For an Eisenstein prime π , N π ≠ 3 , {\displaystyle...
are visible when the period lattice is the Gaussian integer lattice or Eisenstein integer lattice. It has an aspect belonging to the theory of special functions...
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